To simplify the expression [tex]\(\frac{5 \sqrt{2} \pi - 4 \sqrt{2} \pi}{\sqrt{2}}\)[/tex], follow these steps:
1. First, simplify the numerator:
[tex]\[ 5 \sqrt{2} \pi - 4 \sqrt{2} \pi \][/tex]
Combine like terms:
[tex]\[ (5 - 4) \sqrt{2} \pi \][/tex]
Simplifying the expression inside the parentheses:
[tex]\[ 1 \cdot \sqrt{2} \pi = \sqrt{2} \pi \][/tex]
2. Next, simplify the fraction:
[tex]\[ \frac{\sqrt{2} \pi}{\sqrt{2}} \][/tex]
Since [tex]\(\sqrt{2}\)[/tex] in the numerator and the denominator cancel out:
[tex]\[ \pi \][/tex]
So, the simplified form of the expression is [tex]\(\pi\)[/tex].
The estimated value of [tex]\(\pi\)[/tex] is approximately 3.14159 when rounded to five decimal places.
Hence, the correct answers are:
The simplified form of [tex]\(\frac{5 \sqrt{2} \pi - 4 \sqrt{2} \pi}{\sqrt{2}}\)[/tex] is [tex]\(\pi\)[/tex].
Its estimated value is 3.14159.
